Equivariant Homology and Spectral Sequences

Abstract

If a group G operates on a topological space X, then one can define equivariant homology and cohomology groups, which can be thought of heuristic-ally as a “mixture” of H(G) and H(X). This equivariant theory provides a powerful tool for extracting homological information about G from the action of G on X. It is in this way, for example, that Quillen proved his theorem about the Krull dimension of H*(G, ℤp) for G finite (VI.9.8).